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No special abilities for slowing down enemies, but I find Riven pretty good at chasing them down. Her Q ability offers a little bit of extra mobility and a short disable from the knockup, her W ability features a short stun, her E ability is a short sprint, and her R gives her extra range and a ranged execute.

Vayne has increased movespeed when moving toward an enemy champion. Also, she rolls. Also, she can stun.
Tryndamere's taunt reduces the movespeed of enemies that have their back turned. Also, he spins.
Olaf can slow, also cannot be disabled with his ultimate.
Mundo can slow, and can have increased movespeed.
Nasus has a legendary slow, his Wither is a death sentence.
Garen can move very quickly and deal significant damage while moving.
Karthus can slow hard with his Wall of Pain, and continue to barrage with Lay Waste and Defile.
Master Yi will move incredibly fast and cannot be slowed during his ultimate. Alpha Strike also closes the gap.
Shaco can slow, and his passive naturally gives him increased damage to targets facing away. Also, he has a built in flash+stealth.
Skarner/Ashe will apply a slow that can be reapplied indefinitely, while his mana pool lasts. Also, he can suppress.
Teemo can move quickly and applies damage over time.
Rammus gains a massive movespeed boost with his Powerball, which applies a brief stun upon landing, followed up by his taunt, which is pretty much a death sentence.

There's more, but a lot of them with chasing abilities are either situation or skillshots, meaning they aren't as easily applied as the tactics above.

Answering the cleanse question, no, cleanse will not remove warwick's ult, if you look at the listed CC effects it removes, suppress is not listed. (so skarner, urgot, malz, and other ults of that form are also not removed.

Note that no one is going to run from Shaco because he’s Shaco, they’re going to run from him if he gets fed and starts becoming too much to deal with. But this describes almost any carry or assassin in the game so maybe what you want to know is what champions are really hard to get away from.

Any assassin, carry, or mage with a gap closing ability would probably satisfy your playing style. Champs that come to mind are: Akali, Flora, Master Yi, and Kasadin.